The normal force is the push of a surface perpendicular to itself. It balances the part of an object’s weight pressing into the surface and sets how much friction is available. It is smaller on slopes and when you pull upward on an object.
How to use the Normal Force Calculator
- Surface
- Mass m
- Gravitational acceleration g
- Incline angle θ
- External force F (optional)
- Angle of F above the surface φ
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose flat or inclined, enter the mass and (for a slope) the angle. An external force at angle φ above the surface direction reduces the normal force; use a negative angle for a force pushing into the surface.
Tips
- Draw a free-body diagram and list every force before calculating.
- Newton’s second law uses the net force – add forces as vectors.
- Mass is in kilograms; weight is a force in newtons (W = mg).
- Friction always opposes the motion (or the tendency to move).
Common mistakes to avoid
- Confusing mass with weight.
- Forgetting friction or gravity components on a slope.
- Adding forces at different angles as if they were parallel.
Inputs explained
| Field | What to enter |
|---|---|
| Surface | Choose one: Flat, Inclined |
| Mass m | Units: kg, g, mg, t, lb, oz |
| Gravitational acceleration g | Units: m/s², ft/s², g, cm/s² |
| Incline angle θ | Units: °, rad, arcmin, arcsec, mrad |
| External force F (optional) | Units: N, kN, MN, mN, lbf, kgf … |
| Angle of F above the surface φ | Units: °, rad, arcmin, arcsec, mrad |
Example values
How the main result changes when Mass m changes and everything else stays at the example values above:
| Mass m (kg) | Normal force (N) |
|---|---|
| 10 | 98.0665 |
| 15 | 147.0998 |
| 20 | 196.133 |
| 25 | 245.1663 |
| 30 | 294.1995 |
| 40 | 392.266 |
Formula
Flat: N = m·g − F·sin φ · Incline: N = m·g·cos θ − F·sin φWorked example
Inputs — Surface: Flat; Mass m: 20 kg; Gravitational acceleration g: 9.80665 m/s²; External force F (optional): 0 N; Angle of F above the surface φ: 30 °.
Results — Normal force = 196.133 N; Weight = 196.133 N; Weight component along the surface = 0 N.
Key terms
- Normal force
- Contact force perpendicular to a surface.
Frequently asked questions
Is the normal force always equal to the weight?
Only on a flat surface with no other vertical forces.
Why is the normal force smaller on a slope?
Only the component mg·cos θ presses into the surface.
What happens in a lift accelerating upward?
The normal force (your apparent weight) increases.
Can the normal force be zero?
Yes – when the object loses contact, e.g. in free fall.
What formula does the Normal Force Calculator use?
Flat: N = m·g − F·sin φ · Incline: N = m·g·cos θ − F·sin φ.